Integrated operational transconductance amplifier (OTA) circuits are used in a wide array of applications such as filtering or signal level regulation (i.e., gain or attenuation blocks). A commonly used topology for an OTA is given in FIG. 1 of the accompanying drawings. The OTA 100 includes two functional elements: an input voltage-to-current converter 102 characterized by transconductance gm.sub.0 and a programmable linear current scaling circuit 104 with an input to output current gain ratio A.sub.I. The current gain A.sub.I is a function of bias currents I.sub.1 and I.sub.2 as given in the following equation: EQU A.sub.I =k(I.sub.2 /I.sub.1)
where k is a constant of proportionality. The resulting transconductance for the OTA 100 is given by the following equations: ##EQU1##
In the application of the OTA 100 in an integrated transconductance-capacitor (Gm-C) filter, Gm is tuned and/or programmed to achieve some desired bandwidth. The tuning circuit is often a phase lock loop which tunes Gm so that the ratio of Gm/C is some desired value where C is the filter capacitance. For the OTA 100, the bias current I.sub.1 is typically set by the tuning circuit, and I.sub.2 is typically a programmable value that enables linear scaling of the bandwidth with respect to a reference current set by I.sub.1. A common implementation of the OTA 100 uses a current steering digital-to-analog converter (D/A) to set the value for I.sub.2, thus enabling digital programming of the filter bandwidth.
In bipolar or Bipolar-CMOS technology, the current scaling element is typically a bipolar "translinear amplifier" such as the one depicted in FIG. 2 of the accompanying drawings. In bipolar transistor technology, the output current, I.sub.out, of the translinear amplifier 200 is proportional to the exponential of the input voltage, I.sub.out .varies.exp(V.sub.be /V.sub.T), where V.sub.T is the thermal voltage. As a result, the current gain of the bipolar translinear amplifier 200 is exactly proportional to the ratio of I.sub.2 /I.sub.1 as in the first equation. Thus, the desired linear scaling of Gm can be performed by adjusting the I.sub.2 /I.sub.1 ratio.
In MOS technology, however, the output current of the transistor is proportional to the quadratic of the input voltage, I.sub.out .varies.(V.sub.gs -V.sub.T).sup.2 where V.sub.T is the threshold voltage. As a result, the current gain of a MOS translinear amplifier shown in FIG. 3 of the accompanying drawings is not exactly proportional to I.sub.2 /I.sub.1, but is a non-linear function of this ratio. Furthermore, the current gain is also dependent on the nominal value of the input current I.sub.in as well as the carrier mobility, .mu., which is highly process and temperature dependent.
FIG. 4 of the accompanying drawings shows an example of a typical voltage tunable complementary MOS OTA 400 implementing a translinear amplifier current scaling circuit 402, similar to the one shown in FIG. 3. Here the nominal Gm is set by resistor Rgm, and the Gm "tuning" is performed by adjusting the tuning bias voltage, Vtune, to the N-channel MOS differential pairs, MN1, MN2 and MN3, MN4. Bias currents Iss represent the DC biasing for the MOS OTA 400. As a result of the non-linear transistor gain, wide dynamic range current scaling (and consequently Gm scaling) is more problematic for MOS technology than bipolar technology.
Hence, there is a need for a circuit in MOS technology that emulates the linear behavior of the bipolar "translinear amplifier" in order to obtain deterministic scaling of the OTA transconductance.